Non-negatively curved GKM orbifolds

Abstract

In this paper we study non-negatively curved and rationally elliptic GKM${}_4$ manifolds and orbifolds. We show that their rational cohomology rings are isomorphic to the rational cohomology of certain model orbifolds. These models are quotients of isometric actions of finite groups on non-negatively curved torus orbifolds. Moreover, we give a simplified proof of a characterisation of products of simplices among orbit spaces of locally standard torus manifolds. This characterisation was originally proved in [Wiemeler, Torus manifolds and non-negative curvature, arXiv:1401.0403] and was used there to obtain a classification of non-negatively curved torus manifolds.

35 pages; 7 figures; minor changes in v4; to appear in Math. Z

References in corpus (2)

• How is a graph like a manifold?
• Upper bounds for the dimension of tori acting on GKM manifolds

Cited by in corpus (1)

• GKM actions on cohomogeneity one manifolds